BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Two-stage Stochastic Programming with Linearly Bi-parameterized Qu
 adratic Recourse - Jong Shi Pang (University of Southern California)
DTSTART:20190319T154500Z
DTEND:20190319T163000Z
UID:TALK121276@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:This paper studies the class of two-stage stochastic programs 
 (SP) with a linearly bi-parameterized recourse function defined by a conve
 x quadratic program. A distinguishing feature of this new class of stochas
 tic programs is that the objective function in the second stage is linearl
 y parameterized by the first-stage decision variable\, in addition to the 
 standard linear parameterization in the constraints. Inspired by a recent 
 result that establishes the difference-of-convexity (dc) property of such 
 a recourse function\, we analyze the almost-sure subsequential convergence
  of a successive sample average approximation (SAA) approach combined with
  the difference-of-convex algorithm (DCA) for computing a directional deri
 vative based stationary solution of the overall non- convex stochastic pro
 gram. Under a basic setup\, the analysis is divided into two main cases: o
 ne\, the problem admits an explicit\, computationally viable dc decomposit
 ion with a differentiable con- cave component\, based on which the discret
 ized convex subproblems to be solved iteratively can be readily defined\; 
 and two\, an implicit bivariate convex-concave property can be identified 
 via a certain smoothing of the recourse function. The first case includes 
 a strictly convex second-stage objective and a few special instances where
  the second-stage recourse is convex but not strictly convex. A general co
 nvex second-stage recourse function belongs to the second main case\; this
  case requires the introduction of the notion of a generalized critical po
 int to which the almost-sure subsequential convergence of the combined SAA
  and DCA is established. Overall\, this research provides the first step i
 n the investigation of this class of two-stage SPs that seemingly has not 
 been\, until now\, the object of a focused study in the vast literature of
  computational two-stage stochastic programming.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR